Problem: John read the first $114$ pages of a novel, which was $3$ pages less than $\dfrac13$ of the novel. Write an equation to determine the total number of pages $(p)$ in the novel. Find the total number of pages in the novel.
Explanation: Let $p$ be the total number of pages in the novel. We can represent $\dfrac13$ of the novel as $\dfrac13p$. John has read $3$ fewer pages than $\dfrac13p$. He has read $\dfrac13p-3$ pages. Since he has read $114$ pages, let's set this equal to $114$ : $ \dfrac13p-3=114$ Now, let's solve the equation to find the total number of pages $(p)$ in the novel. $\begin{aligned} \dfrac13p-3&=114\\ \\ \dfrac13p-3{+3}&=114{+3}&&{\text{add }3} \text{ to each side}\\ \\ \dfrac13p&=117\\ \\ \dfrac{\dfrac13p}{{\dfrac13}}&=\dfrac{117}{{\dfrac13}}&&\text{divide each side by ${\dfrac13}$}\\ \\ p&=351\end{aligned}$ The equation is $\dfrac{1}{3}p-3 = 114$. The novel has a total of $351$ pages.